Solve for $x$ and $y$ using elimination. ${x-6y = -43}$ ${-x-5y = -45}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-11y = -88$ $\dfrac{-11y}{{-11}} = \dfrac{-88}{{-11}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {x-6y = -43}\thinspace$ to find $x$ ${x - 6}{(8)}{= -43}$ $x-48 = -43$ $x-48{+48} = -43{+48}$ ${x = 5}$ You can also plug ${y = 8}$ into $\thinspace {-x-5y = -45}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(8)}{= -45}$ ${x = 5}$